neat stuff.
8:

• asper
• pares
• parse
• pears
• rapes
• reaps
• spare
• spear

Comments : you seem to never use $length for anything interesting -- just as an added layer of complexity to your %word hash. You can remove it when referring to %words keys and achieve the same results :
push @{$word{$sorted_word}}, $_;
and so on.
Also, you can replace

@most_ref=();
push @most_ref, \@{$word{$length}{$sorted_word}};
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with

@most_ref=(\@{$word{$sorted_word}});
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